andrederiverten
Andrederiverten denotes the second derivative of a function, the derivative of its first derivative. If a function f is differentiable on an interval and its derivative f' is differentiable there, the second derivative exists and is written as f''(x) = d^2f/dx^2. It measures how quickly the slope of f is changing.
Example: for f(x) = x^3, f'(x) = 3x^2 and f''(x) = 6x.
Interpretation: The sign of f'' indicates concavity: f''(x) > 0 means f is concave up at x; f''(x)
Relationship to curvature: for a graph y = f(x) with a continuous second derivative, the curvature κ at
Notation and higher order derivatives: f'' can also be denoted f^(2)(x). Higher derivatives include f''' and beyond.
See also: derivative, higher-order derivative, Taylor series, inflection point, curvature.
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